As some others have said, don't bother with SF. San Francisco is a long way from Mammoth, you have to drive to Reno, then down. You can't cut through the mountains in the winter. SF to Mammoth is at least 7 hours, possibly more. It makes more sense to fly into Reno, Mammoth, or LA.
I live down south, and ski Mammoth 2-3 weekends a month. From Newport Beach it is a 5 hour 15 minute drive leaving at 4 am. Flying into Mammoth is sketchy, that airport is dangerous, but lots of people are doing it now.
Reno might seem like the best option, but the route from Reno to Mammoth goes over some passes that go up to 8600 feet. It would be really tough in a blizzard.
I would probably fly into LA or Mammoth. Reno is 3 hours away, and might be a lot more if the weather is bad. LA is easy to fly into, and the drive has no real weather potential until you actually get to Mammoth, the whole way up is in a valley, not mountains. If the flight to Mammoth does not sketch you out, then go that route.
LA is 5 hours, but almost definitely that. Reno is 3, but could be a lot more. I would go for LA.